Method for determining the position, notably  in terms of elevation, of a target flying at  very low altitude

ABSTRACT

The present invention relates to a method for determining the position notably the elevation of a target flying at very low altitude. An electromagnetic detection system extracts the measurement of the elevation on the basis of the amplitude of the interference signal produced by a signal emitted directly by the target and by a signal emitted by the target towards the ground then reflected by the ground towards the radar. Embodiments of the invention can notably be used within the framework of the guidance of drones in the final landing phase.

BACKGROUND OF THE INVENTION

The present invention relates to a method for determining the positionnotably the elevation of a target flying at very low altitude. Thisinvention can notably be used within the framework of the guidance ofdrones in the final landing phase.

BRIEF DESCRIPTION OF THE PRIOR ART

The guidance of a drone in the landing phase makes it necessary tolocate it in an accurate manner so as to calculate its trajectory up tothe touchdown point on the runway and to correct its trajectorythroughout the landing phase. To this end a system composed of a radar,at least one ground beacon and at least one beacon on board the dronecan be implemented. The objective of this system is to improve locationaccuracy. However, elevational location of the drone is subject toinaccuracies, related to the presence of multiple reflections of thesignal emitted by the target on the ground. The interferences related tothe reflection of the signal on the ground are particularly significanton account of the small value of the angle of incidence of the droneduring the landing phase.

Location results are generally improved by filtering the signalsreflected by the ground as well as by minimizing the contribution ofthese signals by optimizing the orientation and directivity of the radarantenna beam.

For this purpose, a first solution consists in reducing the width of theantenna beam and in pointing the latter towards the target, so as tominimize the contribution of the signal reflected by the ground byplacing the pathways reflected by the ground in throughs of the antennapattern. This solution is conceivable only if the constraints weighingon the dimension of the antenna and its physical installation are nottoo significant. Indeed it requires bulky and expensive hardware. Infact this solution is rarely used in a context where for example amobile radar must be available.

Other solutions are known for improved locating of a target flying atvery low altitude in the event of multiple reflections. Among thelatter, the following solutions can be used alone or in a mutuallycomplementary manner.

For example, a second solution consists in using high-resolutionadaptive processing operations on the signal received. These processingoperations exhibit the twofold drawback of being difficult to implementand of giving poor results if the assumptions made about the model vary,even very slightly. Furthermore, they demand significant calculationcapability, thereby increasing the cost of the system.

A third solution resides in the increase in the distance and Dopplerresolution. However, this increase in resolution can only be effected ifthe radar is positioned at a sufficiently high level relative to theground. This is not always possible having regard to the context of usewhich greatly constrains the height of radar antennas, again forexample, for a mobile radar.

A fourth solution is aimed at increasing the diversity of the emissionfrequencies. Nevertheless, diversifying the frequencies makes itnecessary to employ a significant frequency span in order for this to beeffective. This is often incompatible with the application involved and,additionally, is not always authorized by the agencies that allocate thefrequencies.

SUMMARY OF THE INVENTION

An aim of the invention is notably to alleviate the aforesaid drawbacks.For this purpose, the subject of the invention is a method fordetermining the elevation of a target close to the ground by anelectromagnetic detection system. This method extracts the measurementof the elevation on the basis of the amplitude of the interferencesignal produced by a signal emitted directly by the target and by asignal emitted by the target towards the ground then reflected by theground towards the radar. The system emits a detection signal towardsthe target. The interference signal is produced by the signal re-emitteddirectly by the target and the signal re-emitted by the target towardsthe ground then reflected by the ground towards the detection system.The reception antenna is composed for example of arrays of radiatingelements. The interference signal received by this antenna can besampled at the level of the sub-arrays. The measurement of the elevationis then established on the basis of the amplitude of the sampledinterference signal. The sub-arrays each correspond for example to aline of radiating elements and can be disposed in a horizontal, paralleland uniform manner over the antenna as a whole. The sub-arrays can alsobe situated in a substantially vertical plane. The frequency f of thesampled signal is for example the value which minimizes the followingfunction:

${J(U)} = {\sum\limits_{i,k}{{r_{i + k} + r_{i - k} - {2r_{i}{\cos \left( {2\pi \; {Uk}\; \Delta} \right)}}}}}$

with

-   -   r_(i+k) representing the result of the subtraction between the        value of the signal received at the level of the sub-array of        order i+k and the value of the signal received at the level of        the sub-array of order i+k+1, r_(i−k) representing the result of        the subtraction between the value of the signal received at the        level of the sub-array of order i−k and the value of the signal        received at the level of the sub-array i−k−1,    -   Δ representing the distance between the phase centres of two        consecutive sub-arrays.

The ratio between the height h₂ of the target relative to the ground andthe distance d projected on the ground between the radar and the targetis expressed as a function of the frequency f of the interference signalcalculated according to the following relation: h₂/d=λf/2 where λ is thewavelength of the signal emitted.

Advantageously the elevation height h₂ can be determined for non-planeand non-horizontal ground on the basis:

-   -   of the point of reflection R of the signal re-emitted by the        target towards the ground on the latter,    -   of the elevation height determined for plane and horizontal        ground.

The expression of the equality between the angles of incidence of theray re-emitted by the target towards the ground and that reflected bythe ground with the tangent plane to the ground at the reflection pointmakes it possible to obtain the coordinates (x_(R), z_(R)) of thereflection point R as well as the angle α_(R) between the tangent planeto the ground at the point R and the horizontal on the basis of thefollowing cost function:

${{C(r)}} = {{\frac{h_{1} - z_{R} + {x_{R} \times \alpha_{R}}}{x_{R}} - \frac{h_{2}}{d - x_{R}}}}$

where h₁ represents the height relative to the ground of the antenna, h₂represents the estimation of the elevation height calculated in the caseof plane and horizontal ground, the values (x_(R), z_(R), α_(R))minimizing this function are the coordinates of the reflection point R.

Obtaining the value of the angle α_(R) between the tangent plane at R tothe terrain and the horizontal allows notably to correct the height ofthe target relative to the tangent plane to a value H₂ in the followingmanner: H₂=h₂+z_(R)+(d−x_(R))×α_(R), h₂ being the calculated height ofthe target relative to the ground in the case of plane and horizontalground and d being the projected distance on the ground of the targetfrom the antenna.

The processing according to the invention can thereafter be improved bya CHA processing.

The antenna used can also be a sparse antenna.

The target can comprise an active emitter or else behave as a passivereflector. The target can be a drone in the landing phase.

The comparison of the amplitude of the reflection coefficient with afixed threshold is for example performed previously. The height h₂ ofthe target can then be determined by a processing of monopulse type ifthe value of the amplitude of the reflection coefficient is less thanthis threshold.

The invention has notably the main advantages that it accommodatesexisting radar models, that it can be implemented on various types ofantennas, that it uses processing that is simple to implement and thatit requires insignificant calculation means.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will becomeapparent with the aid of the description which follows, offered inconjunction with the appended drawings which represent:

FIG. 1, an aircraft in the landing phase where the elements of a deviceused by the method of the invention are depicted,

FIG. 2, the phenomenon of reflection of the image of the targetsubsequent to the emission of a radar wave,

FIG. 3, the antenna pattern constituted by the target and its image,

FIG. 4 a, the interference signal received at antenna level,

FIG. 4 b, the minimum and maximum amplitudes of the interference signalreceived at antenna level,

FIG. 5, the various processing phases of the method,

FIG. 6, an exemplary sampling of the signal received by amplitude over ½a period,

FIG. 7, an exemplary sampling of the signal received by amplitude over1/7^(th) of a period,

FIG. 8 a, the reflection phenomenon due to the image of the target inthe case of a horizontal ground,

FIG. 8 b, the reflection phenomenon due to the image of the target inthe case where the ground is not horizontal,

FIG. 9, the reflection phenomenon in the case where the ground isneither plane nor horizontal.

DETAILED DESCRIPTION

FIG. 1 presents an aircraft 1 in the phase of landing on a runway 2.This aircraft, for example a drone, is guided by a system composed of aradar 3, a beacon 4 on board the drone, and a beacon 5 on the ground.This guidance system is notably described in French patent applicationNo. 04 12313. To participate in the guidance of the aircraft 1, theradar must know the position of the latter, that is to say its azimuthaland elevational coordinates. For this purpose, the radar emits a signal6 towards the aircraft 1, that will be called the target subsequently.The target can behave either as a passive reflector or as an emitter byvirtue of the onboard beacon 4. The description of the present inventionconsiders the case of the use of an emitter on board the target, but theinvention can apply equally well in the case of a passive emitter.

It has been indicated previously that signals re-emitted by the targetcould additionally be reflected on the ground before being picked up bythe radar. The state of the runway 2 may be such that the reflection isquasi-specular, these reflections producing outlying measurements.

FIG. 2 illustrates the paths of the signals re-emitted by the target 1in a direct and indirect manner. In this figure, only the antenna 21 ofthe radar 3 is represented. This antenna can be used inemission/reception or in reception only. In this example, the antenna 21is an array antenna termed complete that is to say it consists of Nsub-arrays 22 spaced out regularly in the vertical plane and complyingwith the necessary interdistance conditions so as not to createambiguous lobes. The present invention can additionally apply also inthe case of a sparse antenna. Each of the sub-arrays of the antenna 21corresponds for example to a line of several radiating elements, whoseresultant corresponds to a phase centre in the elevation plane.

In FIG. 2, the sub-arrays are represented by lines consisting ofradiating elements which receive a signal of like phase in relation tothe elevation plane. These lines may be horizontal as is the case inFIG. 2 or else non-horizontal. Subsequently, the lines are considered tobe horizontal.

In order to simplify the diagram, only the radiations emitted and/orreceived by a sub-array 23 are represented. The corresponding line 23 issituated at a height h₁ relative to the ground. This line emits and/orreceives a signal 24 towards the target 1. The target, for its part, issituated at a height h₂ from the ground and at a distance projected onthe ground d from the radar. The resultant signal, re-emitted by thetarget, is composed inter alia of the following signals picked up by theline 23:

-   -   on the one hand a direct signal 25 which heads off towards the        line 23 and forms with the horizontal an angle θ_(c) also named        the angle of elevation of the target seen from the radar,    -   on the other hand a signal 26 itself reflected by the ground 30.

The latter signal 26 is reflected in a quasi-specular manner by theground. It reflects as a signal 27 towards the line 23. The angle θ_(i)formed between the signal 27 reflected by the ground and the horizontalis called the angle of elevation of the image seen by the radar.Specifically, the signal 27 reflected by the ground can be regarded as asignal 28 emitted by the image 29 of the target relative to the ground.The system thus consisting of the target and its image forms atarget-image dipole. The signal picked up by the line 23 is thereforecomposed of the signal 25 re-emitted by the target and of the signal 27re-emitted by the image.

FIG. 3 represents a wide-beam antenna pattern of the surveillance radartype. More particularly, this figure illustrates the modelled antennapattern corresponding to a dipole composed of the target 1 and of itsimage 29. This modelling amounts to interpreting the entirety of thesignal, of sinusoidal form, originating from the target-image bipole atthe level of the antenna as if it were a signal re-emitted by apointlike system situated at the centre of the dipole.

The physical quantities characterizing the pattern at a given instantare as follows:

-   -   d: the distance projected on the ground between the target and        the radar,    -   θ: the angle of sight relative to the horizontal plane of the        ground,    -   h₁: the height relative to the ground of the line considered on        the antenna,    -   h₂: the height of the target relative to the ground.

The interference pattern resulting from the previously describedmodelling of the re-emitted signal is of the form, to within amultiplicative constant:

|I(θ)|²=1+ρ²+2ρ cos((4πh ₂ sin(θ))/λ)+φ)  (1)

Where

-   -   ρ represents the amplitude of the ground reflection coefficient,    -   φ is a phase shift between the incident signal and the signal        re-emitted,    -   λ is the wavelength of the signal emitted.

Given that the radar antenna is situated close to the ground, that thetarget is in the landing phase, and therefore that it too is situatedclose to the ground, its height relative to the ground is thereforesmall compared with the distance d and it is therefore possible toconsider that the values of the angle θ are small. This therefore makesit possible to simplify equation (1) so as to obtain the followingformula for the interference, by likening sin(θ) to θ:

|I(θ)|²=1+ρ²+2ρ cos((4πh ₂θ)/λ)+φ)  (2)

If h₁ is the height of a line of the antenna, still for small values ofθ, we have the following relation:

h ₁ =d×θ  (3)

Which gives the following form for equation (2):

|I(h ₁)|²=1+ρ²+2ρ cos((4πh ₂ h ₁)/λd)+φ)  (4)

This relation (4) expresses the shape of the interference curve as afunction of the height h₁.

FIG. 4 a illustrates the interference signal 41 produced by the directsignal 25 and the reflected signal 27 at the level of the antenna 21such as expressed by relation (4). The invention utilizes thisinterference signal 41 present at the level of the antenna. Moreparticularly, the method according to the invention extracts the heighth₂ from this interference signal. This interference signal is composedof a constant part 1+ρ² and of a sinusoid dependent on the height of thetarget h₂.

The method according to the invention advantageously uses the existenceof such an interference signal 41 at the level of the antenna, theamplitude and the period of this signal not being known a priori. Tocharacterize this signal, a sampling 42: S₁, S₂, S_(N), is performed atthe level of the radiating lines 22, 23 of the antenna. The sampling canbe performed in a spatially regular manner if the distance Δ between twoconsecutive radiating lines is constant. It may also be adapted to anon-uniform array of lines. The sampling may therefore depend on thestructure of the antenna.

FIG. 5 illustrates the various possible steps for determining the heighth₂ on the basis of the interference signal 41.

A first step 51 makes it possible to determine the value of theamplitude of the ground reflection coefficient ρ. The minimum andmaximum amplitudes, illustrated in FIG. 4 b, of the interference signalare given by the following relations: I_(max)=(1+ρ)² and I_(min)=(1−ρ)².Consequently, the ratio of the minimum and maximum amplitudes is givenby

${\frac{I_{\min}}{I_{\max}} = \frac{\left( {1 - \rho} \right)^{2}}{\left( {1 + \rho} \right)^{2}}},$

from which the amplitude of the reflection coefficient is deduced:

ρ=(1−√{square root over (Imin/Imax)})/(1+√{square root over(Imin/Imax)})  (6)

Once the value of ρ has thus been calculated, in a second step 52, thisvalue is compared with a given threshold which may be fixed for exampleat 0.5. If the value of ρ is less than this threshold, it is consideredthat there is no interference due to the reflection of the signalreflected by the ground. The target is then located in terms ofelevation by means of a conventional off-boresight processing 53 ofmonopulse type for example. In the converse case where a reflection dueto the target-image dipole is indeed detected, a processing adapted tothe signal resulting from the target and from its image is performed.

This processing begins with a step 54 of spatial sampling of the signalreceived on each of the antenna lines such as illustrated for example inFIG. 4 a. This sampling advantageously requires few values, it cannotably be carried out for about ten values. Hereinafter, the number ofsamples collected will be represented by n.

In a following step 55, the spatial frequency of the interference signalwill be estimated on the basis of the sampling of the signal carried outin the previous step. The basic principle of the determination of thefrequency is as follows:

Let V be a generic signal of the form:

V(x)=cos(2πfx+φ)  (7)

With:

-   -   φ, representing an unknown,    -   x, the position of a line on the array of the antenna    -   f, the frequency of the signal received.

In order to estimate the frequency f of the global signal received, weconsider for example a set of n samples represented by the quantityS=(s₁, . . . , s_(n)) of the interference signal V(x) sampled on thepositions x_(i)=x₀+iΔ with i taking the values from 1 to n, x₀representing the position of an arbitrary line serving as reference onthe antenna and Δ being the sampling stepsize corresponding to thedistance between two consecutive radiating lines. Thus for any twolines, the following relation is obtained on the basis of equation (7),regardless of i and regardless of k:

s _(i+k) +s _(i−k)=cos(2πfx _(i+k)+φ)+cos(2πfx _(i−k)+φ)  (8)

Now, by sampling x_(i+k)=x_(i)+kΔ and likewise x_(i+k)=x_(i)−kΔ.

Relation (8) then becomes, regardless of i and regardless of k:

s _(i+k) +s _(i−k)=cos(2πfx _(i)+φ+2πfkΔ)+cos(2πfx _(i)+φ−2πfkΔ)  (9)

Then with the aid of the following relation

cos(X−Y)+cos(X+Y)=2 cos(X)cos(Y)  (10)

the relation

S _(i+k) +S _(i−k)=2 cos(2πfx _(i)+φ)cos(2πfkΔ)  (11)

is obtained on the basis of (9).

Since according to equation (7), s_(i)=cos(2πfx_(i)+φ), the followingrelation is therefore obtained:

s _(i+k) +s _(i−k)=2s _(i) cos(2πfkΔ)  (12)

which leads to the following equation:

s _(i+k) +s _(i−k)−2s _(i) cos(2πfkΔ)=0  (13)

By solving this equation it is possible to obtain an estimation of f.This estimation is obtained by minimizing the function J defined by:

$\begin{matrix}{{J(W)} = {\sum\limits_{i,k}{{s_{i + k} + s_{i - k} - {2s_{i}{\cos \left( {2\pi \; {Wk}\; \Delta} \right)}}}}}} & (14)\end{matrix}$

f is then estimated by the value of W₀ which minimizes the functional J.Let:

$\begin{matrix}{{\min\limits_{W}{J(W)}} = {J\left( W_{0} \right)}} & (15)\end{matrix}$

The estimate {circumflex over (f)} of f is then given by:

$\begin{matrix}{\hat{f} = {{\arg\left( {\min\limits_{W}{J(W)}} \right)} = W_{0}}} & (16)\end{matrix}$

Within the framework of the problem treated, a model of the re-emittedsignal originating from the target-image bipole may be as follows:

E(x)=A+α cos(2πfx+φ)+b(x)  (17)

where (φ,A,α) are unknown and b(x) represents Gaussian white noise withvariance σ².

In this case, we consider n samples of this signal

$R = {\begin{bmatrix}{r_{1} = {E\left( {x_{0} + {1\; \Delta}} \right)}} \\\vdots \\{r_{n} = {E\left( {x_{0} + {n\; \Delta}} \right)}}\end{bmatrix}.}$

The samples of the Gaussian white noise are assumed to be mutuallyindependent and of like variance σ². They will therefore be neglectedsubsequently.

A first step consists for example in eliminating the constant term Arepresenting the amplitude of the interference signal 41 present at thelevel of the antenna so as to reduce to a model of the sinusoid plusnoise type.

To this end an estimator of the following form can be used:

$\begin{matrix}{\hat{A} = {\frac{1}{2}\left( {{\min\limits_{i = {\lbrack{1,11}\rbrack}}r_{i}} + {\max\limits_{i = {\lbrack{1,11}\rbrack}}r_{i}}} \right)}} & (18)\end{matrix}$

The samples R are expressed as a function of the estimator Â of A. Thisleads to the samples

$R_{Bis} = \begin{bmatrix}{r_{1} - \hat{A}} \\\vdots \\{r_{n} - \hat{A}}\end{bmatrix}$

to which is applied the previously explained basic principle ofdetermining f. In the same manner, f is therefore estimated byminimizing the following functional:

$\begin{matrix}{{J(U)} = {\sum\limits_{i,k}{{r_{i + k} + r_{i - k} - {2r_{i}{\cos \left( {2\pi \; {Uk}\; \Delta} \right)}}}}}} & (19)\end{matrix}$

The sought-after value of f is the value which minimizes the functionJ(U).

It should be noted that some of the n samples retained should be closeto the minimum and to the maximum of the signal so as to obtain a goodestimation Â of A. In the converse case, the estimation Â might bebiased notably if the n measurement points cover less than one period ofthe signal. This is highlighted in the example which follows.

By way of example, n samples of the signal 17 received on the antennaare used for each result, with for example n=11. The form of the signalpresented is as follows:

E(x)=A+α cos(2πfx+φ)+b(x)  (17)

In each of FIGS. 6 and 7, the abscissa 60 represents the n samples, andthe ordinate 61 the amplitude A of the interference signal present atthe level of the antenna. Each figure presents the results of estimatingA for two different samples. The first FIG. 6 uses two samplings 63 and64 carried out on ½ a reference signal period. The results 65 and 66obtained respectively for the samples 63 and 64 give estimations of Awhich differ by nearly 10%.

The second FIG. 7 uses over 7/10^(th) of a period two samplings 70 and72 giving respectively the results 71 and 73 for the estimated value ofA. The difference between the two results is here of the order of 4%.

This shows clearly that the results of the estimation of A may bestrongly biased if the samples cover only a small part of the period ofthe signal. This therefore also gives rise to a significant error in theestimation of f. It is therefore necessary for the samples used to bechosen correctly, this not always being possible.

This is why, in a preferential manner, the constant term A can beeliminated by direct subtraction of the signal received on one line fromthe signal received on the next line. A new sampling R′ of the followingform is thus obtained:

$R^{\prime} = {\begin{bmatrix}{r_{1}^{\prime} = {r_{1} - r_{2}}} \\{r_{2}^{\prime} = {r_{2} - r_{3}}} \\\vdots \\{r_{n - 1}^{\prime} = {r_{n - 1} - r_{n}}}\end{bmatrix}.}$

The processing operations for estimating f are thereafter the same asthose described previously.

Once the estimation has been obtained for f, the next step 56 makes itpossible to obtain the ratio h₂/d, the height of the target over thedistance between the radar and the target projected on the ground, inthe following manner:

By considering as phase and amplitude reference at a given instant thedirect path for the first line, the latter receives a signal of valueS₁:

S ₁=1+ρ×e ^(jφ) ×e ^(−j(2π/λ)2(h) ¹ ^(h) ² ^(/d))  (20)

With:

-   -   ρ: the modulus of the ground reflection coefficient    -   φ: the phase of the ground reflection coefficient    -   λ: the wavelength of the signal emitted by the target

The assumptions are as follows:

ρ and φ are constant for the n re-emitted signals,

-   -   θ_(c) is identical for the n direct signals (it is assumed that        the signals are parallel)

By putting Δ for the distance between the first and the second line, thesignal received by the second line of the array is expressed in thefollowing manner:

S ₂ =e ^(j(2π/λ)Δ×sin(θc))(1+ρ×e ^(jφ) ×e ^(−j(2π/λ)2(h) ² ^((h) ¹^(+Δ)/d)))  (21)

Which gives for the (k−1)^(th) line:

S _(1+k) =e ^(j(2π/λ)k×Δ×sin(θc))(1+ρ×e ^(jφ) ×e ^(−j(2π/λ)2(h) ² ^((h)¹ ^(k×Δ)/d)))  (22)

And therefore for the k^(th) line:

S _(k) =e ^(j(2π/λ)(k−1)×Δ×sin(θc))(1+ρ×e ^(jφ) ×e ^(−j(2π/λ)2(h) ²^((h) ¹ ^(+(k−1)×Δ)/d)))  (23)

The modulus of the signal received for each line is therefore given bythe following relation:

|S _(k)|² =S _(k) ×S* _(k)=1+ρ²+2ρ cos((2π/λ)2(h ₂(h₁+(k−1)×Δ)/d)+φ)  (24)

By putting φ′=(2π/λ)2(h₂(h₁−a)/d)+φ, the following relation is obtained:

|S _(k)|²=1+ρ²+2ρ cos((2π/λ)2(h ₂ ×k×Δ)/d)+φ′)  (25)

This relation reveals an amplitude modulation on the height of theantenna whose frequency f depends directly on the height of the targetrelative to the ground:

f=2h ₂ /λd  (26)

thereby giving the ratio of the height of the target to the distanceprojected on the ground between the radar and the target as follows:

h ₂ /d=λf/2  (27)

The ratio h₂/d is therefore defined for a given value of the wavelengthλ.

The objective of the last step 57 is notably to give an estimation ofthe height of the target as well as angles of elevation.

By considering that the target deploys at very low altitude, the anglesof elevation have notably a small value. Thus, an estimation d′ of d canbe obtained, for example by a radar measurement. This estimation d′, onaccount of the small value of the angles, can be regarded as the radialdistance r between the phase centre of the radar antenna and the target.This distance r being measured by the radar. The error incurred bymaking this estimation tends moreover to decrease as the targetapproaches the ground.

The angles of elevation described in FIG. 2 are determined by thefollowing equations obtained by construction:

-   -   for the angle of elevation θ_(c) of the target seen by the        radar:

$\begin{matrix}{\theta_{c} = {{artctg}\left( {\frac{h_{2}}{d} - \frac{h_{1}}{d^{\prime}}} \right)}} & (28)\end{matrix}$

-   -   for the angle of elevation θ_(i) of the image seen by the radar:

$\begin{matrix}{\theta_{i} = {- {{artctg}\left( {\frac{h_{2}}{d} + \frac{h_{1}}{d^{\prime}}} \right)}}} & (29)\end{matrix}$

The ratio h₂/d having been calculated in the previous step, the anglesθ_(c) and θ_(i) are easily calculated.

Additionally, once θ_(c) has been determined, h₂ is deduced therefrom inthe following manner:

h ₂ =r sin(θ_(c))+h ₁  (30)

r being the radial distance measured by the radar antenna.

Equations (28), (29), (30) therefore make it possible to obtain theestimated values of θ_(c), θ_(i), and h ₂.

FIGS. 8 a and 8 b highlight the difference between the results obtainedin the case where the ground is horizontal and in the case where it isnot. FIG. 8 a represents the case of a horizontal ground and notably thequantities characteristic of the elevation: θ_(c), θ_(i), and h₂. Theprinciple of constructing the quasi-specular reflection of the rayre-emitted by the target 26 is that the angles of incidence of thesignal 26 and of reflection of the signal 27 relative to the plane ofreflection are assumed to be equal to an angle α₁. The height h₂, whichcomes into the previous equations, corresponds in reality to the heightof the target relative to the plane of reflection, which here coincideswith the ground, and not to the height of the target relative to theground vertically. If FIG. 8 b is considered, when the ground is nothorizontal, the image of the target does not have the same position asin FIG. 8 a. Specifically, the image is the symmetric projection of thetarget relative to the plane of reflection which, in the case of FIG. 8b, is not horizontal. The height h₂ of the target relative to the planeof reflection will therefore be different in the case of non-horizontalground. The estimation of the elevation may thus be biased and it may benecessary to refine the result.

FIG. 9 represents the reflection phenomenon in the presence of non-planeand non-horizontal ground 90, the profile of the ground between theradar and the target being known. The following elements of FIGS. 1 and2 are represented in the figure:

-   -   the target 1 represented in a pointlike manner,    -   the line 23 of the antenna situated at a height ha from the        ground,    -   the radial distance r between the radar and the target,    -   the horizontal distance d between the radar and the target,    -   the signal 24 emitted by the line 23 and re-emitted as a signal        25 in a direct manner by the target 1,    -   the signal 26 re-emitted towards the ground by the target and        its reflection 27 on the ground.

The height H₂ represents the height of the target relative to thetangent plane 91 to the ground at a point R called the reflection point.Determining the reflection point entails calculating its position in thereference frame of the radar. The position of R is characterized by itscoordinates x_(R) and z_(R) respectively in relation to the horizontalaxis 93 and the vertical axis 94 as well as by the angle α_(R) formedbetween the slope 91 of the ground at this point and the horizontal 92.

The profile of the ground is assumed known, thereby affording access tothe knowledge of z_(R) and α_(R) for all the potential positions of thepoint R, that is to say z_(R)=f(x_(R)), the function f being known, andα_(R)=g(x_(R)), the function g also being known. The principle used tocalculate the coordinates of the point R is based on the fact that theangles of reflection and of incidence of the signal re-emitted by thetarget towards the ground are equal at this point. They are representedrespectively in the figure by the angles α₁ and α₂. By considering theangles to be small, the following assumption is made: tan(α)=sin(α)=α, αbeing any one of the angles represented in the figure. By constructionand by making the assumption stated above the following relations areobtained for α₁ and α₂:

$\begin{matrix}{\alpha_{1} = \frac{h_{1} - z_{R} + {x_{R} \times \alpha_{R}}}{x_{R}}} & (31) \\{\alpha_{2} = \frac{h_{2}}{d - x_{R}}} & (32)\end{matrix}$

As α₁=α₂, the following relation is then obtained:

$\begin{matrix}{\frac{h_{1} - z_{R} + {x_{R} \times \alpha_{R}}}{x_{R}} = \frac{h_{2}}{d - x_{R}}} & (33)\end{matrix}$

with h₁ the height of the antenna relative to the ground and h₂, theelevation height calculated in the case of plane and horizontal ground.

The coordinates of the point R are obtained by minimizing the followingcost function:

$\begin{matrix}{{{C(R)}} = {{\frac{h_{1} - z_{R} + {x_{R} \times \alpha_{R}}}{x_{R}} - \frac{h_{2}}{r - x_{R}}}}} & (34)\end{matrix}$

The coordinates thus obtained of the point R make it possible to definethe tangent plane to the ground at the reflection point, or plane ofreflection, which is subsequently regarded as the ground itself so as toreduce the case of non-plane and non-horizontal ground to the case ofnon-horizontal ground which is simpler to treat.

Once the coordinates of the point R have been calculated and notably theangle α_(R), a correction is applied to the elevation height obtainedfor plane and horizontal ground. The height h₂ relative to thehorizontal ground then becomes the height H₂ relative to the plane ofreflection. This height H₂ is given by the following relation:

H ₂ =h ₂ +z _(R)+(d−x _(R))×α_(R)  (36)

where d represents the distance between the target and the radar,projected onto the horizontal 92. The corrected value for the height ofthe target relative to the plane of reflection for non-plane andnon-horizontal ground is thus obtained.

The estimation thus obtained for the elevation can advantageously beimproved by an amplitude phase correlation calculation of the signalreceived with a predefined replica also named CHA or Correlation HeightAlgorithm.

One of the advantages of the method according to the invention is toimprove elevational location while preserving a constant antennadimension, and a possibility of surveillance in an extended angulardomain. The stability of the results obtained in the domain of coveragewithout lobe widening and without fading is also appreciable.

Moreover, the simplicity of the processing implemented allows itsapplication at lower cost. It also requires a reasonable calculationcapability given that it is possible to limit the number of receptionchannels. Specifically a small number of measurements suffices to obtaina good estimation of the elevation.

Another advantage of the invention is that the method can be usedequally well on a complete array antenna and on a sparse antenna.Moreover it can be applied equally well for an antenna comprisinguniform or non-uniform arrays.

In the exemplary implementation of the invention, the antenna forreceiving the signals re-emitted by the target corresponds to theantenna of the radar emitting the detection signal. This antenna couldbe different from the emission antenna.

1. Method for determining by an electromagnetic detection system anelevation of a target close to a ground, comprising the steps of:receiving, by a reception antenna, a first signal emitted directly by atarget; receiving, by the reception antenna, a second signal emitted bythe target towards the ground then reflected by the ground toward theelectromagnetic detection system; and determining the of the target froman amplitude of an interference signal produced by the first signal andby the second signal.
 2. The method of claim 1, further comprising thesteps of: emitting a detection signal towards the target, wherein thesignal re-emitted directly by the target is the first signal, and thesignal re-emitted by the target towards the ground then reflected by theground is the second signal.
 3. The method of claim 1, wherein thereception antenna comprises a plurality of sub-arrays of radiatingelements, the method further comprising the steps of: sampling theinterference signal at the level of the sub-arrays, to produce a sampledinterference signal; and determining the elevation based on theamplitude of the sampled interference signal.
 4. The method of claim 3,wherein the sub-arrays comprise a line of radiating elements disposed ina substantially horizontal, parallel and uniform manner over thereception antenna as a whole.
 5. The method of claim 3, wherein thesub-arrays are situated in a substantially vertical plane.
 6. Methodaccording to claim 3, wherein a frequency f of the sampled signal is avalue which minimizes the following a function:${J(U)} = {\sum\limits_{i,k}{{r_{i + k} + r_{i - k} - {2r_{i}{\cos \left( {2\pi \; {Uk}\; \Delta} \right)}}}}}$wherein r_(i+k) is a subtraction between a value of a signal received atsub-array i+k and the value of the signal received at sub-array of orderi+k+1, r_(i−k) is a subtraction between the value of the signal receivedat sub-array i−k and the value of the signal received at sub-arrayi−k−1, and Δ is a distance between the phase centers of two consecutivesub-arrays.
 7. The method of claim 1, further comprising the followingstep: calculating a ratio between an elevation height h₂ of the targetrelative to the ground and a distance d projected on the ground betweenthe electromagnetic detection system and the target according to therelationship: h₂/d=λf/2 where λ is a wavelength of the first signal andf is a frequency of the interference signal.
 8. The method of claim 7,further comprising the following step: obtaining the coordinates (x_(R),z_(R)) of a reflection point R and an angle α_(R) between the tangentplane to the ground at the point R and the horizontal on the basis of acost function:${{C(r)}} = {{\frac{h_{2} - z_{R} + {x_{R} \times \alpha_{R}}}{x_{R}} - \frac{h_{2}}{d - x_{R}}}}$wherein: h₁ represents the height relative to the ground of the antenna,h₂ represents the estimation of the elevation height calculated in thecase of plane and horizontal ground, and the values (x_(R), z_(R),α_(R)) minimizing the cost function are the coordinates of thereflection point R.
 9. The method of claim 8, further comprising thefollowing steps: correcting the height of the target relative to thetangent plane to a value H₂, using the value of the angle α_(R) betweenthe tangent plane at R to the terrain and the horizontal, as:H₂=h₂+z_(R)+(d−x_(R))×α_(R) wherein: h₂ is the calculated height of thetarget relative to the ground in the case of plane and horizontalground, and d is the distance projected on the ground of the target fromthe antenna.
 10. The method of claim 1, further comprising thefollowings step: correlating an amplitude and a phase of the signalreceived with a predefined replica.
 11. The method of claim 1, whereinthe antenna used includes a sparse antenna.
 12. The method of claim 1,wherein the target comprises an active emitter.
 13. The method of claim1, wherein the target includes a passive reflector.
 14. The method ofclaim 1, wherein the target includes a drone in the landing phase. 15.The method of claim 1, further comprising the step of determining aheight h₂ of the target by a monopulse-type process if the value of theamplitude of the reflection coefficient is less than a predeterminedthreshold.
 16. The method of claim 7, further comprising the followingstep: determining the elevation height h₂ for a non-plane andnon-horizontal ground on the basis of a point of reflection R of asignal re-emitted by the target towards the ground on non-horizontalground, or of an elevation height determined for plane and horizontalground.